Bouncing off of the interesting question about how to become a Shabbos Goy, how can a Gentile purchase chametz? There is a lot of information here and everywhere on how Jews can sell their chametz before pesach by contacting a rabbi who will arrange the sale of it to a Gentile, but it is unclear as to how that Gentile is selected or how a Gentile can nominate themselves as a chametz purchaser.
How can an interested Gentile purchase chametz? It can't be as easy as calling up a local rabbi and saying, "Oh hai, I can haz chametz? I has lots moniez and I am teh goyish. Kthxbai!" - or is it? Are there rules that a Gentile must fulfill to qualify as a purchaser (other than being a competent adult Gentile)? Are these rules halachic rules or are they more related to social practices or traditions? E.g. "At this synagogue, our minhag is to sell to the parish priest of St. Peter's Catholic Church. If the priest is halachically Jewish, we sell to Gentile members of the local School Board, working forwards from age of first election to the board. Anyone not on this list can pound sand, no chametz for them."
As it pertains to @msh210 's observation that communities tend to pick the same Gentile every year, that's my understanding too. I strongly suspect that there is no guarantee of an "Equal Chametz Opportunity" (with a logo of an equals sign inside a loaf of bread), but is the process for selecting the purchaser essentially hopelessly opaque, or are there ways for an interested Gentile to "place themselves in the path of chametz" as one might say? For example, are chametz purchasers generally selected from existing Shabbos Goys? Are they usually local clergy of other religions that the Rabbi meets at the local Interfaith Roundtable? Is it expected that the purchaser will be the mayor or a similar local politician? If a community's current chametz purchaser dies, disappears, converts to Judaism, or refuses to purchase chametz any more, how would a Rabbi generally go about finding a new purchaser? Does he hang a "chametz for sale" sign in the synagogue window? Is there an underground social network/pipeline already in place to connect the rabbi with another suitable Gentile? Does he post on Craigslist ("For sale: LEAVEN. In various homes and businesses throughout the Tri-County Area. $5,000 OBO. Money back guarantee!")? Does he cast lots over the phone book and cold-call candidates ("Hello sir, are you a Gentile? Do you know what chametz is? Would you like to help us out by buying some for Passover this year?")? Is it a best practice (or even a minhag) for him to recruit on a college campus, where presumably he is more likely to encounter someone who understands complex business transactions ( @msh210 mentioned the importance of finding someone like that)?
As to why a Gentile would want to do this, I imagine it would be similar to why one might want to become a Shabbos Goy - to build relationships, help others, and have meaningful or interesting adventures.